The entropy gap conjecture for closed hypersurfaces in dimensions at most six

Let $M^n\subset\mathbb{R}^{n+1}$ be a closed hypersurface with $n\leq 6$, and let $\lambda(M)$ denote its entropy. Let $\lambda(\mathbb{S}^n)$ be the entropy of the round sphere. Entropy gap conjecture. The entropy satisfies

$$\lambda(M)\geq\lambda(\mathbb{S}^n).$$

This is the zero-gap version of the entropy gap theorem for closed self-shrinkers and is relevant to understanding singularities of mean curvature flow through the monotonicity of entropy. The conjecture was recently proved by Bernstein and Wang.